WASHINGTON — The House Intelligence Committee approved a bipartisan proposal on Thursday to provide additional resources to help find the cause of Havana syndrome illnesses and take steps to review the C.I.A.'s handling of the mysterious episodes that have injured more than 200 government officials. The measure would overhaul the agency's office of medical services and create a voluntary system where C.I.A. officers assigned overseas could first receive brain scans and lab work that would help doctors determine the extent of their injures should they later exhibit symptoms consistent with Havana syndrome or report being victims of a health episode. The measure comes as some intelligence officers have expressed reticence about accepting foreign posts, or bringing their family members on tours in countries where the episodes have taken place, current and former officials said. "I think as long as these incidents are recurring, with what seems to be increasing frequency, without the identification of a perpetrator and without the ability to stop them, I think those concerns are going to continue," said Representative Adam B. Schiff, Democrat of California and the chairman of the Intelligence Committee. A U.S. official said C.I.A. officers had volunteered in large numbers to work on the issue of the health episodes, eager to find answers. Since 2016, diplomats, intelligence officers and military personnel in Asia, Europe and the Americas have reported hearing strange sounds, feeling unexplained heat or experiencing pressure and then suffering headaches, nausea, vertigo or other symptoms. In many cases, the symptoms have gone on for months or years. While some government officials are convinced that a hostile intelligence service using an eavesdropping device or a directed-energy weapon is responsible for the injuries, C.I.A. analysts have not reached a conclusion about what is causing the episodes or if a hostile power is responsible. While the agency's director, William J. Burns, has been praised for the attention and resources he has put toward victims of Havana syndrome, Congress has been critical of how the C.I.A. and the larger U.S. government handled the cases before this year. The Intelligence Committee is doing its own investigation, and the bill approved on Thursday mandates an inspector general review of the performance of the C.I.A.'s medical division, and sets up an outside advisory board to examine its work. "We want accountability," Mr. Schiff said. "It took too long to get to where we are.